This thesis explores the dynamics of two bipedal, passive-walker models that are free to move in a three-dimensional environment. Specifically, two rigid-bodied walkers that can sustain anthropomorphic gait down an inclined plane with gravity being the only source of energy were studied using standard dynamical systems methods. This includes calculating the stability of periodic orbits and varying the system parameter to create bifurcation diagrams and to address the persistence of a periodic solution under specific parameter variations. These periodic orbits are found by implementing the Newton-Raphson root solving scheme. The dynamical systems associated with these periodic orbits are not completely smooth. Instead, they include discontinuities, such as those produced due to forces at foot contact points and during knee hyper-extension. These discontinuities are addressed in the stability calculations through appropriate discontinuity mappings.

The difference between the two walker models is the number of degrees of freedom (DOF) at the hip. Humans possess three DOF at each hip joint, one DOF at each knee joint, and at least two DOF at each ankle joint. The first walker model studied had revolute joints at the hips and knees and completely locked ankles. To make the walking motion more anthropomorphic, additional degrees of freedom were added to the hip. Specifically, the second walker model has ball joints at the hips.

Two control algorithms are used for controlling the local stability of periodic motions for both walker models. The methods, reference and delay feedback control, rely on the presence of discontinuities in the system. Moreover, it is possible to predict the effects of the control strategy based entirely on information from the uncontrolled system. Control is applied to both passive walker models to try and stabilize an unstable periodic gait by making small, discrete, changes in the foot orientation during gait. Results show that both methods are successful in stabilizing an unstable walking motion for a 3D model with one DOF in each hip and to reduce the instability of the walking motions for the model having more mobility in the hip joints.